Block #339,404

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 2:11:17 AM · Difficulty 10.1278 · 6,470,897 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

186650803e6209daec86bdb156389c726f0dd3f2e7ec2e8d4808483c21b5e7d4

View on Chainz ↗

Height

#339,404

Difficulty

10.127850

Transactions

Size

1.08 KB

Version

Bits

0a20bac0

Nonce

411,270

Timestamp

1/2/2014, 2:11:17 AM

Confirmations

6,470,897

Mined by

⛏️ -aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

cb6ad2e6bcb2800f52b6e4b46a43dc415f1de4fc8cc59a836e6b1b258e12f3bc

Transactions (1)

Coinbasecb6ad2e6bcb280…6b1b258e12f3bc

1 in → 28 out9.7100 XPM1015 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.634 × 10⁹³(94-digit number)

16343235460409738550…95783169631240234239

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.634 × 10⁹³(94-digit number)

16343235460409738550…95783169631240234239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.634 × 10⁹³(94-digit number)

16343235460409738550…95783169631240234241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.268 × 10⁹³(94-digit number)

32686470920819477100…91566339262480468479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.268 × 10⁹³(94-digit number)

32686470920819477100…91566339262480468481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.537 × 10⁹³(94-digit number)

65372941841638954201…83132678524960936959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.537 × 10⁹³(94-digit number)

65372941841638954201…83132678524960936961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.307 × 10⁹⁴(95-digit number)

13074588368327790840…66265357049921873919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.307 × 10⁹⁴(95-digit number)

13074588368327790840…66265357049921873921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.614 × 10⁹⁴(95-digit number)

26149176736655581680…32530714099843747839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.614 × 10⁹⁴(95-digit number)

26149176736655581680…32530714099843747841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #339,404

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